Bistability and chaos at low-level of quanta

TL;DR

This paper investigates quantum bistability and chaos in a single-mode Kerr nonlinear oscillator at low excitation levels, analyzing quantum effects, decoherence, and the quantum-classical transition through Wigner functions and strange attractors.

Contribution

It introduces a detailed analysis of quantum bistability and chaos at few-quanta levels, including minimal excitation thresholds and quantum interference phenomena.

Findings

Quantum chaos regime identified via Wigner functions and strange attractors.

Minimal excitation number for bistability determined.

Quantum interference effects linked to hysteresis and chaos observed.

Abstract

We study nonlinear phenomena of bistability and chaos at a level of few quanta. For this purpose we consider a single-mode dissipative oscillator with strong Kerr nonlinearity with respect to dissipation rate driven by a monochromatic force as well as by a train of Gaussian pulses. The quantum effects and decoherence in oscillatory mode are investigated on the framework of the purity of states and the Wigner functions calculated from the master equation. We demonstrate the quantum chaotic regime by means of a comparison between the contour plots of the Wigner functions and the strange attractors on the classical Poincar\'e section. Considering bistability at low-limit of quanta, we analyze what is the minimal level of excitation numbers at which the bistable regime of the system is displayed? We also discuss the formation of oscillatory chaotic regime by varying oscillatory excitation numbers at ranges of few quanta. We demonstrate quantum-interference phenomena that are assisted hysteresis-cycle behavior and quantum chaos for the oscillator driven by the train of Gaussian pulses as well as we establish the border of classical-quantum correspondence for chaotic regimes in the case of strong nonlinearities.